Our definition agrees with the one considered in both [1]} and [2]}Note that in [3]}, [4]} a different definition of the Gauss-Bonnet term was considered. There, a linear combination of quadratic curvature invariants was considered with the demand that in the Riemannian limit this combination will yield the Riemannian Gauss-Bonnet term. and follows from the contraction of the Riemann tensor with the Riemann double dual after expanding the generalized Kronecker deltas. Let us also stress out that the inclusion of the aforementioned term in Metric-Affine Gravitational Theories is interesting for various reasons. For instance, this term is projectively invariantThis aspect is crucial for constructing healthy Theories [5]}, [6]}. and also this exact linear combination of Riemann squared terms is free of ghosts [3]}, a feature that is not true for general quadratic curvature Theories (see [6]}). In addition, this definition is valid for any dimension and \((\ref {GB})\)  becomes topological as soon as the connection is reduced to be Levi-Civita.
